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The intersection point is the solution. In mathematics, a system of linear equations (or linear system) is a collection of one or more linear equations involving the same variables. [1] For example, is a system of three equations in the three variables x, y, z. A solution to a linear system is an assignment of values to the variables such that ...
Tridiagonal matrix algorithm. In numerical linear algebra, the tridiagonal matrix algorithm, also known as the Thomas algorithm (named after Llewellyn Thomas ), is a simplified form of Gaussian elimination that can be used to solve tridiagonal systems of equations. A tridiagonal system for n unknowns may be written as.
Gauss–Seidel method. In numerical linear algebra, the Gauss–Seidel method, also known as the Liebmann method or the method of successive displacement, is an iterative method used to solve a system of linear equations. It is named after the German mathematicians Carl Friedrich Gauss and Philipp Ludwig von Seidel, and is similar to the Jacobi ...
In mathematics, a matrix ( pl.: matrices) is a rectangular array or table of numbers, symbols, or expressions, arranged in rows and columns, which is used to represent a mathematical object or property of such an object. For example, is a matrix with two rows and three columns. This is often referred to as a "two by three matrix", a " matrix ...
Cramer's rule. In linear algebra, Cramer's rule is an explicit formula for the solution of a system of linear equations with as many equations as unknowns, valid whenever the system has a unique solution. It expresses the solution in terms of the determinants of the (square) coefficient matrix and of matrices obtained from it by replacing one ...
In mathematics, Gaussian elimination, also known as row reduction, is an algorithm for solving systems of linear equations. It consists of a sequence of row-wise operations performed on the corresponding matrix of coefficients. This method can also be used to compute the rank of a matrix, the determinant of a square matrix, and the inverse of ...
Matrix differential equation. A differential equation is a mathematical equation for an unknown function of one or several variables that relates the values of the function itself and its derivatives of various orders. A matrix differential equation contains more than one function stacked into vector form with a matrix relating the functions to ...
Coefficient matrix. In general, a system with m linear equations and n unknowns can be written as. where are the unknowns and the numbers are the coefficients of the system. The coefficient matrix is the m × n matrix with the coefficient aij as the (i, j) th entry: [1] Then the above set of equations can be expressed more succinctly as.